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Existence theorems for monotone operators in reflexive Banach spaces

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Abstract.

In this paper, we obtain an existence theorem for single-valued monotone operators in a reflexive Banach space. Using this result, we prove a fixed point theorem for nonexpansive mappings in a Hilbert space and an existence theorem for maximal monotone operators in a Banach space.

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Authors and Affiliations

  1. Department of Information Engineering, Matsue National college of Technology, Nishi-ikuma-chou, Matsue, Shimane, 690-8518, Japan

    Shin-Ya Matsushita

  2. Department of Mathematical and Computing Sciences, Tokyo Institute of Technology, Oh-Okayama, Meguro-ku, Tokyo, 152-8552, Japan

    Wataru Takahashi

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  1. Shin-Ya Matsushita
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  2. Wataru Takahashi
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Correspondence to Shin-Ya Matsushita.

Additional information

Received: 3 July 2006 Revised: 15 January 2007

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Matsushita, SY., Takahashi, W. Existence theorems for monotone operators in reflexive Banach spaces. Arch. Math. 89, 254–265 (2007). https://doi.org/10.1007/s00013-007-2070-1

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  • DOI: https://doi.org/10.1007/s00013-007-2070-1

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